Multi-scale strategies have been widely used to aggregate hierarchical feature maps in CNN models. Xu et al.[1]} first introduced such strategies into GNNs and proposed jumping knowledge networks, which further improve the accuracy. Inspired by such works, we adopt a multi-scale merge strategy by adding a merge layer in EGATs. Unlike jump knowledge networks, we collect not only node features but also edge features. Edge features will be integrated into nodes in each EGAT layer, result in \(\textbf {H}_m\) , which we mentioned in  REF . All \(\textbf {H}_m\)  generated from different iterations will aggregate together using a concatenation operation. Besides, we adopt the multi-head attention in the merge layer to further stabilize the attention mechanism. Unlike GATs[2]}, our multi-head attention is performed on the unity of all EGAT layers rather than a single layer. \(K\)  independent multi-scale edge-integrated features would be computed and merged, resulting in the feature representation as follows:
\(\vec{h}_i^{*} = \parallel _{k=1}^K (\parallel _{l=1}^Lm_i^{l,k})\) 
